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From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of depression $30 °$ and $45 °$ respectively. Find the distance between the cars.

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237.6 m

273.2 m

356.9 m

283.6 m

answer is B.

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Detailed Solution

Given that, from the top of a tower 100m high, a man observes two cars on the opposite sides of the tower with angles of depression

30 °

and

45 °

respectively.
We have to find the distance between the cars.
In a right-angle triangle,

tan θ = Opposite side Adjacent side

.
Consider the figure,
From the top of a tower 100 m high, a man observes two cars on the opposite of the tower with angles of depression 30â and 45â respectively. Find the distance between the cars. Use[â3=1.73]

From the top of a tower 100 m high, a man observes two cars on the opposite of the tower with angles of depression 30â and 45â respectively. Find the distance between the cars. Use[â3=1.73]

In the right-angle triangle BCA,

tan45 ° = 100 BD ⇒ 1= 100 BD ⇒ BD=100 m

From the right-angle triangle ABD,

tan30 ° = 100 BD ⇒ 13 = 100 BD ⇒ B D=100 3 m ⇒ C D =BC+BD ⇒ C D =100+100 3 ⇒ C D =100(1+ 3)m

\Rightarrow CD = 100 (1 + 1.732)

\Rightarrow CD = 100 (2.732)

\Rightarrow CD = 273.2 m

The distance between the cars is 273.2m
Therefore, the correct option is 2.

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